You may have seen the boxy white building going up in Allston next to Harvard Business School. Well, that’s going to be called the Pagliuca Harvard Life Lab, and it will open in November, thanks to a multimillion-dollar donation from Pagliuca and his wife Judy. Both are alumni of the business school.

The 15,000-square-foot lab will act as incubator space for early-stage life sciences companies founded by Harvard faculty, alumni, students, and postdoctoral scholars. The lab joins a growing portfolio of the university’s innovation spaces on Western Avenue, including the Harvard Innovation Lab (i-lab) and Harvard Launch Lab.

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Now some of you will question if the world’s greatest university really needs another lab, or if we need to worry about Boston’s ability to grow its life sciences sector. Talk about a first-world problem, right?

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Hear the Pagliucas out, and you’ll start to worry too. Sure, it’s hard for other cities to replicate what we have: world-class hospitals, top universities, venture capital, talent. But the market is so hot here there’s a shortage of lab space.

Who gets squeezed out are the people we’re desperately trying to keep: millennials with big dreams.

These are the kids who have started companies and then can’t find lab space to conduct research to discover the next life-saving drug. And when they can, they’re priced out.

The Pagliuca Life Lab will host up to 20 high-potential startups. The first floor consists of co-working space for business meetings, while the second floor will house lab space that is being offered at half the market rate. If you are a student, the space is free.

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Pagliuca, also co-owner of the Celtics, has been in Boston long enough to remember how Route 128 used to be the epicenter of the computer world with Digital Equipment, Wang, Prime, and Data General. Then it wasn’t when personal computers made minicomputers obsolete. The region has since lagged behind Silicon Valley as the country’s premier tech powerhouse.

Pagliuca, who has invested in many companies in his long career at Bain, doesn’t want history to repeat itself.

“We have the natural competitive advantage,” he said in a recent interview, along with Judy, in Bain’s Boston office, “but we have to sustain it.”

Suzanne Kreiter/Globe Staff

The Pagliucas also funded construction of this second-floor lab space.

Harvard began talking to the Pagliucas about funding a life sciences incubator about 18 months ago. The university had launched its i-lab in 2011 for any student at Harvard’s 12 schools to explore entrepreneurship and grow their ventures. That was followed by the Launch Lab in 2014, open to alumni, because some i-lab students wanted to stay on campus after graduation to continue incubating companies.

Nitin Nohria, dean of the Harvard Business School, told me the common refrain he heard was: “This is a great place to talk to people, but I actually can’t do my work here.”

The Pagliucas got it. Around the same time, their daughter-in-law, Felicia Pagliuca, had been a student at Harvard Business School when she cofounded life sciences company
Semma Therapeutics,
which is developing a treatment using stem cells to fight type 1 diabetes.

Judy Pagliuca recalled how Semma struggled to find lab space in Cambridge. Venture-backed and determined, the company ultimately found space.

Steve Pagliuca himself has been a champion of creating a life sciences cluster in Massachusetts in general and in Allston in particular. He began beating the drum in a 2011 Globe op-ed about the need to revive a plan to make Harvard’s Allston campus a new focal point for life sciences. Think of it as Boston’s answer to Cambridge’s Kendall Square.

The Pagliucas are too modest to say how much they donated, but I’m told they gave $15 million to build the Life Lab. They didn’t even want their name on the building, but Harvard insisted because it might inspire other donors.

I got a sneak peek at the new incubator on Monday with a tour led by Jodi Goldstein, who oversees all three of Harvard’s innovation labs. Her office is next door in the i-lab, which gave up part of its parking lot for the Pagliuca building.

The first floor of the Life Lab feels like a tech company where business plans can be hatched on an open floor plan amid neon-colored walls, while the second floor features stark white lab space where scientific experiments take place. Look out the window, and you can see Harvard’s massive Science and Engineering Complex underway, which will help round out the cluster on Western Avenue.

The university recently settled on the inaugural batch of 18 startups. The ventures typically comprise two to five people, and about 44 percent have a female founder. Goldstein said she expects companies to stay on average for about a year.

“Our whole goal is to get them further faster,” she said. “There is no better time to start a company than now.”

Suzanne Kreiter/Globe Staff

The Pagliuca Harvard Life Lab, opening soon, will help the school’s life sciences startups.